Definition of Factors
Factors are numbers which you can multiply together to get another number.
For Example : The numbers 2 and 3 are factors of 6 because 2 x 3 = 6.
A number can have many factors!
Example : 2 and 4 are factors of 8, because 4 x 2 = 8
Also 1 and 8 can also be factors of 8, because 1 x 8 = 8
Therefore 1, 2, 4, 8 are all factors of 8
Common Factor
When more than 2 factors are common between two or more numbers, then this is known as the ‘Common Factor’.
Let’s use an example to understand this.
Let us find the common factors of 12 and 24
12 = 1, 2, 3, 4, 6, 12
24 = 1, 2, 3, 4, 6, 8, 12
After finding the factors for both numbers, we know that the one’s common are 1, 2, 3, 4, 6, 12
Greatest Common Factor
When you find all the factors of two or more numbers, and some factors are common, then the largest of those common factors is the Greatest Common Factor.
This is abbreviated as ‘GCF’. It is also known as Highest Common Factor, also abbreviated as ‘HCF’.
Let’s use an example to find the HCF of the numbers 12 and 30.
First we find the common factors
12 = 1, 2, 3, 4, 6
30 = 1, 2, 3, 6
After finding the common factors, we see that the numbers 6 is the highest common factor of 12 and 30.
Lowest Common Factor
The lowest common factor, is the lowest number that is common to two or more numbers.
If we look at the example used to find the Greatest Common Factor, we see that the lowest common factor for the number 12 and 30 are are 1.
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